论文题目：若干低维小体系中的量子特性研究
作者简介：胡辉，男,1973年04月出生，1996年09月师从于清华大学熊家炯教授，于2001年06月获博士学位。
摘
要
近年来由于纳米加工技术不断进步，使得人们制备以量子点、纳米环、纳米管、磁性纳米颗粒等为代表的低维小体系，以及由它们组成的复合型量子纳米结构的能力，也随之日益增长。低维小体系及其复合结构，因其维度降低和尺寸缩小而呈现出物理内涵极为丰富的量子力学特性，故又被称为受限量子纳米结构。科学家们认为，由固态低维小体系组成的复合受限量子纳米结构，将是直接基于量子力学原理所导致的量子技术所必需的物质基础。目前正处于孕育和萌芽状态之中的量子技术有：量子计算、量子密码、相干量子电子学等。
因此，深入揭示各类低维小体系及其复合结构的量子特性与基本物理规律，了解和掌握对其中量子特性进行人工剪裁和控制的可行性，已成为当前凝聚态物理领域的一个极富生命力的科学前沿。这类基础性研究将推动凝聚态物理学的发展，并为正在兴起的量子技术提供基本原理和可供候选的物理方案。
基于以上的认识，作者在本论文中选择了纳米环等四类低维小体系为对象，深入研究它们的量子特性及物理机制。
论文内容概述
本论文研究了四类低维小体系的量子特性，体系是：半导体纳米环、小金属环中嵌入量子点、Fe8等纳米磁性颗粒及高温d波超导体铜氧面上的磁性杂质体系。这些体系都是1998以后在Science、Nature或Physical Review Letters等高水平刊物上首次发表的新的实验研究体系。我们及时抓住这些新体系开展研究，并将研究重点放在：揭示导致量子特性的物理机制；定性和定量的分析体系的电子性质、光学性质和输运性质；解释已有的实验结果，并进一步预言可能的新物理效应。
本论文分为7章，另有两个附录。第一章及第七章分别为绪言和结论，此处不加赘述。附录1及2中详细介绍了研究磁性问题时所用的解析方法和计算技巧，包括作者对这些方法所做的改进。第二至六章为论文主体部分，分别阐述对以上四类小体系的研究进展。
◎ 第二章针对德国Lorke小组关于纳米环中双电子远红外吸收谱的实验结果，开展理论分析与计算。在理论模型中，首次考察了电子－电子相互作用对这类真实的纳米环双电子体系的能谱和远红外吸收谱的影响，计算结果很好地解释了上述实验结果。在此基础上，还提出了两点预言：一是在外加磁场作用下，电子－电子相互作用将使该体系基态能量随磁场增加而在自旋单态和三态之间交替变化，这种现象非常类似于量子点中的“自旋振荡”效应，可以认为，这种“振荡”将是低维纳米结构的一个共性。二是电子－电子相互作用会杂化纳米环双电子体系的质心运动和相对运动，造成该体系远红外吸收谱中吸收峰的劈裂以及在低能量处的不连续变化。这些预言有待更精密的实验加以论证。
◎ 第三章中提出了一种新的纳米环有效环状束缚势模型，在这个模型基础上，探讨了纳米环激子体系的能谱和光吸收谱，发现纳米环的激子吸收谱和量子点的激子吸收谱有着截然不同的性质：后者的激子吸收峰是等间距分布的，并有相同的幅度，而前者激子吸收峰之间的间距明显不等，并且峰的幅度衰减很快。因而首次从理论上定性解释了2000年H. Petterson et al.相关的实验结果。在此基础上进一步研究了量子尺寸效应和外磁场对激子吸收谱的影响。针对实验室已能制备的真实尺寸的纳米环激子体系，预言了环中激子的Aharonov-Bohm效应。通过对窄宽度纳米环的严格解析计算，揭示出产生这一Aharonov-Bohm效应的基本条件是体系中电子和空穴必须有一定的几率相互分离。鉴于在2000年Lorke小组就已实现对单个纳米环中激子和带电激子的观测，故可以期望这一理论预言在不久的将来获得验证。
◎ 第四章中通过具体的实例，考察了将量子点（或单电子晶体管）嵌入小金属环这一新体系中，量子点中的电子同金属环中的电子之间自旋相互作用所导致的Kondo效应。结果表明，当环的尺度减小到接近于Kondo屏蔽长度这一基本尺度时，Kondo效应强烈地依赖于环的尺度、环中总电子数目被4除的余数以及环内所容纳的磁通大小。还研究了体系中量子点的态密度，并对实验中所能观测的持续电流的行为作出了预言，该预言在两个极限情况下与最近Affleck的解析理论结果符合得很好。
◎ 第五章中，对具有二轴对称性的磁性纳米颗粒，研究了其中由于自旋间交换相互作用和隧穿效应导致的宏观量子相干现象。基于自旋相干态表象中的瞬子（instanton）方法，给出了在难磁化平面内沿任意方向的外磁场作用下，铁磁纳米颗粒中基态隧穿能级劈裂的解析表达式。探讨了磁场角度（指磁场方向和难磁化轴之间的夹角）对拓扑相位干涉效应的影响。发现当磁场角度很小时，基态隧穿能级劈裂随磁场强度的增加发生振荡。这种振荡的幅度随磁场角度的加大而被迅速抑制。解析计算结果和最近在铁磁分子磁体Fe8中实验结果相符合。从反铁磁双子格模型出发，考察了在经典路径附近量子涨落对反铁磁纳米颗粒基态能级劈裂的影响。指出外加磁场不仅对经典作用量中的WKB因子有影响，而且对拓扑相位干涉因子也有一定的作用。这些研究结果为今后对反铁磁分子磁体V8、Fe6或Fe10的实验观测提供了理论依据。
◎ 第六章中以高温超导体中纳米尺度范围内的铜氧面中的磁性杂质为对象，研究了这类体系中磁性杂质对超导体表面传导电子行为的影响。结果表明由于该体系费米面的特殊构型，磁性杂质会诱导出一种新的非费米液体行为。所计算的传导电子在杂质附近的局域态密度分布与最近Pan et al.的实验结果相符。
论文主要成果
◎ 第二、三章对纳米环的研究中主要成果是：理论分析中引入了电子—电子相互作用；提出了一种描述纳米环有效束缚势的新模型。因此，所得理论结果能较好地解释实验现象，并且作出了关于自旋振荡、远红外吸收峰劈裂以及磁场下纳米环中激子的Aharonov-Bohm效应等三个预言。
◎ 第四章研究量子点—小金属环复合体系，发现体系中Kondo效应强烈依赖于环的尺度、电子总数被4除的余数，以及环中磁通的大小，并且预言了Kondo效应辅助的持续电流的性质。
◎ 第五章研究磁性纳米颗粒宏观量子相干现象，给出了有关基态能级劈列的解析表达式。第六章研究磁性杂质在高温超导铜氧面上的影响，发现磁性杂质诱导出一种新的非费米流体行为。
◎ 在理论方法上，本论文注重将解析方法和计算技巧有机地结合，将“分区级数解法”结合精确对角化技术，使之发展成一套较为系统的计算方法，用以有效地求解了几种不同类型的模型哈密顿对应的方程。还推广应用了标准的Anderson模型和Slave-boson平均场方法，较成功地运用到小金属环—量子点和高温超导体铜氧面—杂质这两个截然不同的体系中，得到了有意义的成果。
发表论文及引用情况
作者在研期间共发表学术论文18篇，17篇被SCI收录，1篇被EI收录。其中有3篇发表在Phys. Rev. Lett.上（1篇为第一作者，2篇为第二作者），有6篇发表在Phys. Rev.上（3篇为第一作者，3篇为第二作者）。
迄今有13篇论文被SCI引用59次，其中他引51次；5篇代表性论文被引用41次，其中他引37次，51次他引中包括被Nature上和Phys. Rev. Lett.上的文章他引5次。受到国际同行的关注和肯定。引用请单及主要评价见附件。
关键词：纳米环，激子效应，Aharonov-Bohm效应，Kondo（近藤）效应，宏观量子相干现象。
Abstract
Recently, because of the unprecedented progress in nano-technology, the ability in fabricating the low-dimensional finite systems, such as quantum dots, nanorings, nanotubes, magnetic nanoparticles, as well as their composite structures, has been enhanced rapidly. These low-dimensional systems and their composite structures are also called as confined quantum nanostructures, due to their rich quantum behaviors arising from the reduced dimensionality and the finite size. It has been believed that the composite confined nanostructures, consisting of the solid low-dimensional finite systems, will be the necessary basis of several new quantum technologies developed very recently, for example, quantum computation, quantum cryptography and coherent quantum electronics.
Therefore, it is one of the most valuable research frontiers in the condensed matter physics to reveal the quantum phenomena and basic physics laws in various low dimensional structures and their compositions, and to find and verify the feasibility of controlling these quantum behaviors artificially. This kind of fundamental researches will greatly promote the progress of condensed matter physics, and provide fundamental principles or novel candidate models for the future quantum technology.
Motivated by above expectations, in this dissertation, the author has selected four kinds of the low-dimensional finite systems, including nanorings, as the subjects to study their quantum behavior and physical mechanism in depth.
Contents of the dissertation
In this dissertation, we have studied the quantum properties of four low-dimensional systems: the semiconductor nanorings, the small metallic rings with a side-coupled quantum dot, the magnetic nanopaticles (such as Fe8), as well as the quantum impurity in the surface of the high-temperature d-wave superconductors. These systems, with which the experimental results have been published in the high-quality journals, such as Science, Nature and Physical Review Letters, are the new research objects after 1998. We have focused the theoretical investigation on these systems in time, and emphasized on the following points: the unravel of the inherent physical mechanism responsible for the quantum properties; the qualitative or quantitative analysis of the electronic, optical, and transport properties of the systems; on how to explain the relevant experimental results; and moreover to predict the possible new physical phenomena.
The dissertation is composed of seven chapters and two appendixes. The chapter 1 and chapter 7 are the preface and the conclusion, respectively, and will not be mentioned here in detail. Appendix 1 and 2 are devoted to the detailed description about the analytical treatments and numerical techniques used in solving the magnetic problems. The chapters 2 to 6 are the main parts of the dissertation, in which we have discussed our theoretical results related to the four kinds of systems, respectively.
Ø In chapter 2, we have discussed the effects of electron-electron interaction on the energy levels and far-infrared spectroscopy of a realistic two-electron nanoring. We have revealed two important effects due to the electron-electron interaction: (1) the first one is the intersection between the lowest energy levels. It presents the spin oscillation of the ground state under the magnetic field. This phenomenon is indeed qualitatively similar to that seen in a quantum dot, suggesting its intrinsic nature of zero-dimensional quantum structures; (2) On the other hand, the presence of the electron-electron interaction can lead to the peak splitting and discontinuity in the far-infrared spectrum. Our results provide the first qualitative explanation for the recent experimental measurements by Lorke et al.
Ø In chapter 3, we have proposed a new confinement potential for nanorings and studied the energy levels and absorption spectroscopy of excitons. Compared with the optical properties of excitons in quantum dots, the results provide the first qualitative explanation for the recent experiments reported by Pettersson et al. We have also studied the magnetic field effects on excitons in an InAs nanoring. By numerically diagonalizing the effective-mass Hamiltonian of the problem, which can be separated into terms in center-of-mass and relative coordinates, we calculate the low-lying exciton energy levels and oscillator strengths as a function of the width of the ring and the strength of the external magnetic field. The analytical results are obtained for a narrow-width nanoring in which the radial motion is the fastest one and adiabatically decoupled from the azimuthal motions. It is shown that in the presence of Coulomb correlation, the so-called Aharonov-Bohm effect of excitons exists in a finite (but small) width nanoring. However, when the width of ring becomes large, the non-simply-connected geometry of nanorings is destroyed and in turn yields the suppression of Aharonov-Bohm effect. The conditional probability distribution calculated for the low-lying exciton states allows identification of the presence of Aharonov-Bohm effect. The linear optical susceptibility is also calculated as a function of the magnetic field, to be confronted with the future measurements of optical-emission experiments.
Ø
In
chapter 4, we have investigated the Kondo screening effect generated by a
quantum dot or single-electron transistor embedded in a small metallic ring.
When the ring circumference 
becomes comparable to the fundamental length scale
associated with the bulk Kondo temperature, the Kondo
resonance is strongly affected, depending on the total number of electrons
(modulo 4) and magnetic flux threading the ring. The density of states of the
quantum dot is investigated in detail. The resulting Kondo-assisted persistent
currents are also calculated in both Kondo and mixed valence regimes. Our
numerical results are in good agreement with those of perturbation calculations
by Affleck in the limits of 
and 
.
Ø In chapter 5, the macroscopic quantum coherence of biaxial nano-meter magnets has been investigated. Based on the instanton technique in the spin-coherent-state path-integral representation, we give the analytic expression for the ground-state tunnel splitting of the ferromagnetic magnets under the arbitrarily directed external magnetic field. Our results show that the tunnel splitting oscillates with the field for the small field angle, while for the large field angle the oscillation is completely suppressed. This distinct angular dependence, together with the dependence of the tunnel splitting on the field strengths, provide an independent test for spin-parity effects in biaxial molecular magnets. We also extend above analysis to the biaxial antiferromagnetic magnets in the presence of magnetic field parallel to its hard anisotropy axis. The effects of quantum fluctuations around the classical paths are studied in detail.
Ø
In
chapter 6, we have considered the magnetic impurity effect in optimally doped
cuprate superconductors. Due to the special configuration of the Fermi surface,
a sharp localized resonance above the Fermi energy, characterized by a marginal
Fermi liquid, is predicted for the density of states of the impurity. At the
resonant energies, the spatial distribution of the local conduction electron
density of states around the magnetic impurity is obtained, which is in good
qualitative agreement with the recent measurements of scanning tunneling
microscopy on 
.
Main results of the dissertation
(1) In chapter 2 and 3, the main achievements on nanorings are: the electron-electron interaction was introduced and a new confinement potential for nanorings was proposed in the theoretical analysis. Therefore, the experimental data can be well explained by the theoretical results. We have also made three predictions: the spin-oscillations, the split of the resonance in the far-infrared spectrum, and the Aharonov-Bohm effect for the neutral excitons under the external magnetic field.
(2) In the quantum dot - small metallic ring complex system, we find that the Kondo resonance is strongly affected by the ring circumference, the total number of electrons (modulo 4) and magnetic flux threading the ring in chapter 4. We also predict the property of Kondo-assisted persistent currents.
(3) In chapter 5, we have systematically studied the macroscopic quantum coherence in the magnetic nanoparticles (nano-meter magnets) and obtained the explicitly analytic expression for the ground-state tunnel splitting. In chapter 6, the magnetic impurity effect in optimally doped cuprate superconductors is considered and a marginal Fermi liquid behavior due to the magnetic impurity is predicted.
(4) In the theoretical treatment, we have emphasized on the tight combination of the analytic derivations and numerical simulation techniques. In particular, we have developed a practical numerical technique composed of the series expansion method and exact diagonalization technique, in solving several different kinds of model Hamiltonians. We have generalized the standard Anderson impurity model and slave-boson mean-field method. Moreover, we have applied them successfully to two distinctively different systems: the side-coupled ring and quantum dot system, and the quantum impurity embedded in the high Tc superconductors, and have obtained useful results.
The status of publications and citations
During working on the subjects, the author has published 18 scientific papers, among which 17 papers have been included by SCI, and 1 by EI. In particular, 3 papers have been published in Phys. Rev. Lett. (1 paper as the first author and 2 as the second author), and 6 papers in Phys. Rev. (3 paper as the first author and 3 as the second author).
Till now totally 13 papers are cited by SCI as many as 59 times, of which 51 by others. 5 representative papers are cited by 41 times, of which 37 cited by others, including 5 citations by papers in Nature and Phys. Rev. Lett.. This strongly suggests that our works have been noticed and accepted by the international research groups working in the same direction. The detailed status of the citation and a brief evaluation can be found in the appended files.
Key words: nanorings, exciton, Aharonov-Bohm effect, Kondo effect, macroscopic quantum coherence.
